Semigroup C*-algebras arising from graphs of monoids
Operator Algebras
2022-12-06 v3 Functional Analysis
Group Theory
Abstract
We study groupoids and semigroup C*-algebras arising from graphs of monoids, in the setting of right LCM monoids. First, we establish a general criterion when a graph of monoids gives rise to a submonoid of the fundamental group which is right LCM. Moreover, we carry out a detailed analysis of structural properties of semigroup C*-algebras arising from graphs of monoids, including closed invariant subspaces and topological freeness of the groupoids as well as ideal structure, nuclearity and K-theory of the semigroup C*-algebras. As an application, we construct families of pairwise non-conjugate Cartan subalgebras in every UCT Kirchberg algebra.
Keywords
Cite
@article{arxiv.2111.11151,
title = {Semigroup C*-algebras arising from graphs of monoids},
author = {Cheng Chen and Xin Li},
journal= {arXiv preprint arXiv:2111.11151},
year = {2022}
}
Comments
32 pages; final version (minor changes), accepted for publication in Int. Math. Res. Not